A Nonlinear Corner-Balance Spatial Discretization for Transport on Arbitrary Grids

Abstract

A strictly positive spatial discretization method for the linear transport equation is presented. This method, which is algebraically nonlinear, enforces particle conservation on subcells and approximates the spatial variation of the source in each subcell as an exponential. The method is described in slab geometry and analyzed in several limits of practical significance; numerical results are presented. An x-y-geometry version of the method is then presented, assuming a spatial grid of arbitrary polygons; numerical results are presented. A rapidly convergent method for accelerating the iterations on the scattering source is also presented and tested. The analyses and results demonstrate that the method is startlingly accurate, especially on shielding-type problems, even given coarse and/or distorted spatial meshes.